scholarly journals Approximate pricing formula to capture leverage effect and stochastic volatility of a financial asset

2021 ◽  
pp. 102072
Author(s):  
Youssef El-Khatib ◽  
Stephane Goutte ◽  
Zororo S. Makumbe ◽  
Josep Vives
Keyword(s):  
Stochastic Volatility ◽  
Leverage Effect ◽  
Financial Asset ◽  
Pricing Formula

A CLOSED-FORM PRICING FORMULA FOR EUROPEAN EXCHANGE OPTIONS WITH STOCHASTIC VOLATILITY

2021 ◽  
pp. 1-10
Author(s):  
Puneet Pasricha ◽  
Anubha Goel
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stochastic Volatility Model ◽  
Strike Price ◽  
Volatility Model ◽  
Exchange Options ◽  
Pricing Formula ◽  
Exchange Option

This article derives a closed-form pricing formula for the European exchange option in a stochastic volatility framework. Firstly, with the Feynman–Kac theorem's application, we obtain a relation between the price of the European exchange option and a European vanilla call option with unit strike price under a doubly stochastic volatility model. Then, we obtain the closed-form solution for the vanilla option using the characteristic function. A key distinguishing feature of the proposed simplified approach is that it does not require a change of numeraire in contrast with the usual methods to price exchange options. Finally, through numerical experiments, the accuracy of the newly derived formula is verified by comparing with the results obtained using Monte Carlo simulations.

scholarly journals PERAMALAN VOLATILITAS SAHAM MENGGUNAKAN MODEL EXPONENTIAL GARCH DAN THRESHOLD GARCH

2019 ◽  
Vol 8 (4) ◽  
pp. 309
Author(s):  
SITI RAHAYU NINGSIH ◽  
I WAYAN SUMARJAYA ◽  
KARTIKA SARI
Keyword(s):  
Asset Returns ◽  
Financial Data ◽  
Stock Index ◽  
Garch Models ◽  
Leverage Effect ◽  
Financial Asset ◽  
Asymmetric Volatility ◽  
High Volatility ◽  
Financial Asset Returns ◽  
Forecasting Volatility

In financial data there is asymmetric volatility, which denotes the different movements on conditional volatility of increase and decrease financial asset returns. The exponential GARCH and threshold GARCH models can be used to capture asymmetric volatility, called leverage effect. The aim of this research is to determine the best model between exponential GARCH and threshold GARCH models, and to know the results of forecasting volatility the LQ-45 stock index using the best model. The research showed that the best model to predicting volatility is EGARCH(2,1), because it has the smallest AIC value compared to other models. Then forecasting volatility of the LQ-45 stock index using EGARCH(2,1) showed that volatility increase from the first period until fourteenth period, this means that it has high volatility.

scholarly journals Cross-Commodity Spot Price Modeling with Stochastic Volatility and Leverage For Energy Markets

2013 ◽  
Vol 45 (02) ◽  
pp. 545-571 ◽  
Author(s):  
F. E. Benth ◽  
L. Vos
Keyword(s):  
Stochastic Volatility ◽  
Simulation Method ◽  
Energy Markets ◽  
Stochastic Volatility Model ◽  
Spot Price ◽  
Leverage Effect ◽  
Order Structure ◽  
Spot Prices ◽  
Volatility Model ◽  
Multivariate Stochastic Volatility

Spot prices in energy markets exhibit special features, such as price spikes, mean reversion, stochastic volatility, inverse leverage effect, and dependencies between the commodities. In this paper a multivariate stochastic volatility model is introduced which captures these features. The second-order structure and stationarity of the model are analyzed in detail. A simulation method for Monte Carlo generation of price paths is introduced and a numerical example is presented.

scholarly journals Pricing European options with stochastic volatility under the minimal entropy martingale measure

2015 ◽  
Vol 27 (2) ◽  
pp. 233-247 ◽  
Author(s):  
XIN-JIANG HE ◽  
SONG-PING ZHU
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Martingale Measure ◽  
Minimal Entropy Martingale Measure ◽  
Volatility Model ◽  
In Series ◽  
Expected Utility Maximization ◽  
Equivalent Martingale ◽  
The One ◽  
Pricing Formula

In this paper, a closed-form pricing formula in the form of an infinite series for European call options is derived for the Heston stochastic volatility model under a chosen martingale measure. Given that markets with the stochastic volatility are incomplete, there exists a number of equivalent martingale measures and consequently investors face a problem of making a choice of appropriate measure when they price options. The one we adopt here is the so-called minimal entropy martingale measure shown to be related to the expected utility maximization theory (Frittelli 2000 Math. Finance10(1), 39–52) and the financial rationality for choosing this measure will be further illustrated in this paper. A great advantage of our newly-derived pricing formula is that the convergence of the solution in series form can be proved theoretically; such a proof of the convergence is also complemented by some numerical examples to demonstrate the speed of convergence. To further show the validity of our formula, a comparison of prices calculated through the newly derived formula is made with those obtained directly from the Monte Carlo simulation as well as those from solving the PDE (partial differential equation) with the finite difference method.

Sign in / Sign up

Export Citation Format

Share Document